Sir Alex Ferguson's side are at home to Mick McCarthy's team who won the Championship title last season.
Tottenham, who lost last season's final 4-1 on penalties to United at Wembley, are away to Preston.
League One outfit Leeds have been handed a glamour tie with Liverpool, while big-spending Manchester City host Fulham.
The competition's lowest-ranked side Port Vale face a trip to Scunthorpe.
Full third round draw:
Arsenal v West Brom;
Chelsea v QPR;
Bolton v West Ham;
Barnsley v Burnley;
Hull v Everton;
Leeds v Liverpool;
Manchester United v Wolves;
Manchester City v Fulham;
Sunderland v Birmingham;
Peterborough v Newcastle;
Carlisle v Portsmouth;
Nottingham Forest v Blackburn;
Stoke v Blackpool;
Scunthorpe v Port Vale;
Preston v Tottenham;
Aston Villa v Cardiff.
Ties to be played week commencing September 21
Source: Team_Talk